Diffractive optical device including grating elements with different grating periods and duty ratios

ABSTRACT

A diffractive optical device includes a substrate for allowing transmission therethrough of light to be diffracted; and a grating section located on the substrate and including a plurality of grating elements each having multiple discrete phase levels. The plurality of grating elements are arranged at different grating periods in different areas of a surface of the substrate and have the phase levels in different numbers in accordance with the grating period.

This application is a continuation of application Ser. No. 08/323,927,filed Oct. 17, 1994, now U.S. Pat. No. 5,561,558.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a diffractive optical device,especially a diffractive optical device preventing reduction in thediffraction efficiency even in an area having a small grating period.

2. Description of the Related Art

A diffractive optical device, which utilizes diffraction of light, has agrating pattern for diffraction. The grating pattern is formed byarranging a plurality of grating elements on a substrate. Thediffraction efficiency, which is the ratio of light which can bediffracted with respect to the light incident on the diffractive opticaldevice, is determined by the grating pattern. Generally, how high thediffraction efficiency can be is a matter of a prime importance indetermining the quality of the diffractive optical device.

One of conventional diffractive optical devices is a diffractivemicrolens used for diffracting light which is incident thereonvertically. Briefly referring to FIGS. 1 and 2, such a conventionaldiffractive microlens 100 will be described. FIG. 1 is a plan view ofthe microlens 100 illustrating a grating pattern thereof, and FIG. 2 isa cross sectional view of the microlens 100. The microlens 100 includesa substrate 11. Light which is incident vertically on a bottom surfaceof the substrate 11 is collected or collimated above the substrate 11.As is shown in FIG. 1, a plurality of grating elements 18 are arrangedconcentrically on a top surface of the substrate 11 to form a gratingpattern. A period at which the grating elements 18 are arranged(hereinafter, referred to as a "grating period") becomes progressivelysmaller toward the outer periphery of the substrate 11. As is shown inFIG. 2, each grating element 18 has a rectangular cross section.

FIG. 3 is a cross sectional view of another diffractive microlens 200proposed by J. Jahns and S. J. Walker in "Two-dimensional array ofdiffractive microlenses fabricated by thin film deposition", AppliedOptics Vol. 29, No. 7, pp. 931-936 (1990). The microlens 200 includes asubstrate 11 and a plurality of grating elements 28 arranged on a topsurface of the substrate 11. Each grating element 28 has multiplediscrete phase levels. In the example shown in FIG. 3, each gratingelement 28 has four phase levels including the top surface of thesubstrate 11. Adopting such a way of counting, each grating element 18in the microlens 100 in FIG. 2 has two phase levels. This way ofcounting the phase levels of the grating elements will be usedthroughout this specification.

While the diffractive microlens 100 has a diffraction efficiency of 41%,the microlens 200 has a diffraction efficiency of as high as 81%. It hasbeen found that the larger the number of phase levels of the gratingelement is, the higher the diffraction efficiency is. For example, thediffraction efficiency is 95% where each grating element has eight phaselevels, and the diffraction efficiency is 99% where each grating elementhas 16 phase levels.

Considering the above-described relationship between the diffractionefficiency and the number of phase levels, it is easily assumed that anytype of diffractive optical devices show such relationship.

In the case that light is incident at an angle which is offset withrespect to the vertical direction to the substrate, it is true that thelarger the number of phase levels is, the higher the diffractionefficiency is in an area where the grating period is relatively large.The researchers including the inventors of the present invention havefound that the diffraction efficiency is significantly reduced as thenumber of the phase levels is increased in an area where the gratingperiod is relatively small, namely, proximate to the wavelength of theincident light.

Further, in an area where the grating period is small, precisionprocessing is difficult to perform. Accordingly, it is substantiallyimpossible to process the grating elements into a desirable shape, whichreduces the optical characteristics of the diffractive optical device.

SUMMARY OF THE INVENTION

One aspect of the present invention relates to a diffractive opticaldevice including a substrate for allowing transmission therethrough oflight to be diffracted; and a grating section located on the substrateand including a plurality of grating elements each having multiplediscrete phase levels. The plurality of grating elements are arranged atdifferent grating periods in different areas of a surface of thesubstrate and have the phase levels in different numbers in accordancewith the grating period.

In one embodiment of the invention, the number of the phase levelsbecomes progressively smaller in accordance with decrease in the gratingperiod.

In one embodiment of the invention, the number of the phase levels is atleast 3 in an area where the grating period is at least a first valueobtained by multiplying a wavelength of the light by a first prescribednumber. The number of the phase levels is 2 in an area where the gratingperiod is less than the first value. The first prescribed number issubstantially between 1.5 and 3.

In one embodiment of the invention, the grating section has a duty ratioof substantially between 0.15 and 0.5 in the area where the gratingperiod is less than the first value.

In one embodiment of the invention, the number of the phase levels is atleast 4 in an area where the grating period is at least a second valueobtained by multiplying the wavelength of the light by a secondprescribed number. The number of the phase levels is 3 in an area wherethe grating period is smaller than the second value and at least thefirst value. The second value is substantially between 2 and 5 andgreater than the first prescribed number.

In one embodiment of the invention, the number of the phase levels is atleast 5 in an area where the grating period is at least a third valueobtained by multiplying the wavelength of the light by a thirdprescribed number. The number of the phase levels is 4 in an area wherethe grating period is smaller than the third value and at least thesecond value. The third value is substantially between 4 and 7 andgreater than the second prescribed number.

In one embodiment of the invention, the grating elements have differentheights in accordance with the number of the phase levels thereof.

In one embodiment of the invention, the bottommost level among themultiple discrete phase levels is the surface of the substrate.

In one embodiment of the invention, the smallest grating period isgreater than 1/2 n of the wavelength of the light where n is therefractive index of the substrate, and the duty ratio of the gratingsection changes in accordance with the grating period.

In one embodiment of the invention, the grating elements aresymmetrically arranged with respect to the center thereof and are arckedin an identical direction, and the grating period becomes progressivelysmaller in the direction.

In one embodiment of the invention, the plurality of grating elementsare extended in straight lines in an identical direction, and thegrating period changes in a direction which is perpendicular to thedirection in which the grating elements are extended.

In one embodiment of the invention, the grating section is covered witha thin film.

In one embodiment of the invention, the thin film is reflective.

In one embodiment of the invention, the thin film is non-reflective.

In one embodiment of the invention, the substrate includes a light guideregion for propagating the light.

Another aspect of the present invention relates to a diffractive opticaldevice including a substrate for allowing transmission therethrough oflight to be diffracted; and a grating section located on the substrateand including a plurality of grating elements. The plurality of gratingelements are arranged at different grating periods in different areas ofa surface of the substrate. The smallest grating period is greater than1/2 n of the wavelength of the light where n is the refractive index ofthe substrate. The grating section has a duty ratio changing inaccordance with the grating period.

In one embodiment of the invention, the duty ratio is less than 0.5 inan area where the grating period is less than three to four times thewavelength of the light.

In one embodiment of the invention, the duty ratio becomes progressivelysmaller in accordance with decrease in the grating period.

In one embodiment of the invention, the plurality of grating elementshave different heights in accordance with the grating period.

In one embodiment of the invention, the height of the plurality ofgrating elements becomes progressively smaller in accordance withdecrease in the grating period in an area where the grating period isless than three to four times the wavelength of the light.

In one embodiment of the invention, a part of the plurality of gratingelements each have at least three discrete phase levels.

Thus, the invention described herein makes possible the advantages ofproviding a diffractive optical device which has a high diffractionefficiency in the entire area thereof for the light which is incidentthereon at an angle offset with respect to the vertical directionthereto and which has grating elements easily fabricated even with asmall grating period.

These and other advantages of the present invention will become apparentto those skilled in the art upon reading and understanding the followingdetailed description with reference to the accompanying figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plan view of a conventional diffractive optical device fordiffracting light which is incident vertically thereto;

FIG. 2 is a cross sectional view of the conventional diffractive opticaldevice shown in FIG. 1;

FIG. 3 is a cross sectional view of another conventional diffractiveoptical device for diffracting light which is incident verticallythereto;

FIG. 4 is a cross sectional view of a diffractive optical device in afirst example according to the present invention;

FIG. 5 is a plan view of the diffractive optical device shown in FIG. 4;

FIG. 6 is a cross sectional view of the diffractive optical device shownin FIG. 4 illustrating how light advances;

FIG. 7 is a graph illustrating the relationship between the first orderdiffraction efficiency and the normalized grating period in areas inwhich grating elements have two and three phase levels in thediffractive optical device shown in FIG. 4;

FIG. 8 is a plan view of a diffractive optical device in a secondexample according to the present invention;

FIG. 9 is a cross sectional view of a diffractive optical device in athird example according to the present invention;

FIG. 10 is a graph illustrating the relationship between the first orderdiffraction efficiency and the normalized grating period in areas inwhich grating elements have two through five phase levels in thediffractive optical device shown in FIG. 9 when the incident angle ofthe light is 20°;

FIG. 11 is a graph illustrating the relationship between the first orderdiffraction efficiency and the normalized grating period in areas inwhich grating elements have two through five-phase levels in thediffractive optical device shown in FIG. 9 when the incident angle ofthe light is 30°;

FIG. 12 is a cross sectional view of a diffractive optical device in afourth example according to the present invention;

FIG. 13 is a plan view of the diffractive optical device shown in FIG.12;

FIG. 14 is a graph illustrating the relationship between the first orderdiffraction efficiency and the normalized grating period in areas inwhich duty ratios are 0.3, 0.4 and 0.5 in the diffractive optical deviceshown in FIG. 12 when the incident angle of the light is 20°;

FIG. 15 is a graph illustrating the relationship between the first orderdiffraction efficiency and the normalized grating period in areas inwhich duty ratios are 0.3, 0.4 and 0.5 in the diffractive optical deviceshown in FIG. 12 when the incident angle of the light is 30°;

FIG. 16 is a graph illustrating the relationship between the duty ratioand the normalized grating period with respect to the diffractiveoptical device shown in FIG. 12 when the incident angle of the light is20°;

FIG. 17 is a cross sectional view of the diffractive optical deviceshown in FIG. 12 illustrating how light advances;

FIG. 18 is a plan view of a diffractive optical device in a fifthexample according to the present invention;

FIG. 19 is a cross sectional view of a diffractive optical device in asixth example according to the present invention;

FIG. 20 is a graph illustrating the relationship between the efficiencyof first order diffraction and the normalized grating period in areashaving different duty ratios and different heights in the diffractiveoptical device shown in FIG. 19;

FIG. 21 is cross sectional view of a diffractive optical device in amodification according to the present invention having a reflectivefilm;

FIG. 22 is a cross sectional view of a diffractive optical device inanother modification according to the present invention having aplurality of grating elements connected together at the bottom thereof;and

FIG. 23 is a cross sectional view of a diffractive optical device instill another modification according to the present invention having aplurality of grating elements formed using a positive resist.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereinafter, the present invention will be described by way ofillustrative examples with reference to the accompanying drawings.

EXAMPLE 1

Referring to FIGS. 4 through 7, a diffractive optical device 10 in afirst example according to the present invention will be described. FIG.4 is a cross sectional view of the diffractive optical device 10, andFIG. 5 is a plan view thereof.

As is shown in FIGS. 4 and 5, the diffractive optical device 10 includesa substrate 1 and a grating section 2 located on a top surface of thesubstrate 1. The substrate 1 and the grating section 2 are formed of amaterial which allows transmission therethrough of light of at least awavelength to be diffracted (for example, light having a wavelength of0.6328 μm). The substrate 1 and the grating section 2 may be formed ofdifferent materials from each other or may be integrally formed of anidentical material.

The grating section 2 includes a plurality of grating elements 21arranged so as to form a grating pattern. Each grating element 21 has across section having a plurality of steps, namely, has multiple phaselevels.

The diffractive optical device 10 is used, for example, as an off-axislens as is shown in FIG. 6. An axis of light incident on an off-axislens is different from an axis of light outgoing from the off-axis lens.As is shown in FIG. 6, light 5 which is propagated zigzag in a lightguide region 12 in the substrate 1 goes out through the top surface ofthe substrate 1 as outgoing light 6. The light guide region 12 isprovided with reflective layers 4A and 4B respectively on a top surfaceand a bottom surface thereof for reflecting the light 5 alternately inrepetition. Thus, the light 5 is propagated zigzag from the negativeside to the positive side of axis y and is incident on the gratingsection 2 at an incident angle of which is offset with respect to thevertical direction to the top surface of the substrate 1. Then, thelight 5 is transmitted through the grating section 2 and goes out toabove the substrate 1 vertically. Herein, "goes out vertically" meansthat the axis of the outgoing light 6 is substantially vertical to thetop surface of the substrate 1, namely, parallel to axis z. By utilizinga part of the substrate 1 as the light guide region 12, the size of anoptical system of the diffractive optical device 10 in the direction ofaxis z is significantly reduced.

The grating section 2 has a grating pattern as shown in FIG. 5 in orderto collect the light 5 incident at an offset angle at point 3 which isaway from the top surface of the substrate 1 by distance f. Each gratingelement 21 forming the grating pattern is arcked while projecting towardthe positive direction of axis y. The grating period is progressivelyreduced and the curvature of the grating elements 21 is progressivelyincreased toward the positive direction of axis y. Such a gratingpattern will be described in detail later. At point 3, an optical datarecording medium such as an optical disc may be placed. In such a case,at least a part of the outgoing light 6 is reflected by the optical datarecording medium and thus returns to the diffractive optical device 10.The light reflected by the optical data recording medium is guided to alight detector. Needless to say, the diffractive optical device 10 canbe used for various other uses.

Although one substrate is used in one diffractive optical device in FIG.6, one substrate may be commonly used for a plurality of diffractiveoptical devices by providing a plurality of grating sections 2 on thetop surface, on a bottom surface, or on both of the top and the bottomsurfaces of the substrate 1. Other types of optical devices utilizing nodiffraction effect such as a laser light source or a light detector mayalso be provided on the substrate 1.

As is shown in FIG. 4, the grating section 2 is divided into two areas:area 2A where the grating period is relatively small and area 2B wherethe grating period is relatively large. The grating period of area 2A issmaller than 1.6 times the wavelength of the incident light, and thegrating period of area 2B is at least 1.6 times the wavelength of theincident light. In this example, each grating element 21 in area 2 hasthree phase levels while each grating element 21 in area 2A has twophase levels. In more detail, each grating element 21 in area 2Bincludes a first level having a height of 0 from the top surface of thesubstrate 1, a second level having a height of 1/2 h_(B), and a thirdlevel having a height of h_(B). Each grating element 21 in area 2Aincludes a first level having a height of 0 from the top surface of thesubstrate 1 and a second level having a height of h_(A).

According to the experiment performed by the inventors of the presentinvention, the diffraction efficiency at three phase levels was higherthan that at two phase levels in area 2B having a relatively largegrating period. In area 2A having a grating period proximate to thewavelength of the incident light, the diffraction efficiency at threephase levels was rapidly reduced; and the diffraction efficiency at twophase levels was reduced at a smaller ratio or even raised.

With reference to FIG. 7, the above-mentioned experiment will bedescribed in detail. FIG. 7 is a graph illustrating the relationshipbetween the normalized grating period Λ/λ and the diffractionefficiency. Symbol Λ denotes the grating period, and symbol λ denotesthe wavelength of the light. The experiment was performed under theconditions that the incident angle θ of the light was 20° and therefractive index n of areas 2A and 2B was 1.5. As is indicated by thesolid line in FIG. 7, in the case of the grating elements each havingthree phase levels, the diffraction efficiency is more than 50% in area2B having a relatively large grating period but is reduced drasticallyin area 2A where the grating period is proximate to the wavelength ofthe incident light. As is indicated by the dashed line, in the case ofthe grating elements each having two phase levels, the diffractionefficiency is 30 to 40% in area 2B but increases as the grating perioddecreases. Especially from the point at which the grating period isapproximately twice or three times the wavelength of the incident light,the diffraction efficiency rapidly increases as the grating perioddecreases. For example, where the grating period is 1.6 times thewavelength of the incident light, the diffraction efficiency of thegrating elements having two phase levels is equal to the diffractionefficiency of the grating elements having three phase levels.Accordingly, for example, by providing the grating elements 21 havingthree phase levels in an area where the grating period is at least 1.6times the wavelength of the incident light and providing the gratingelements 21 having two phase levels where the grating period is lessthan 1.6 times the wavelength of the incident light, the diffractionefficiency can be high in the entire diffractive optical device 10.

As is described above, there was a problem conventionally in thatprecision processing was difficult to perform in an area of a gratingperiod proximate to a wavelength of incident light, and thus it wasdifficult to shape grating elements having many phase levels in anintended manner, causing deterioration in the optical characteristics.Since it has been found by the inventors of the present invention thatthe optimum number of phase levels decreases as the grating perioddecreases. Accordingly, even the diffractive optical devices having anarea where the grating period is small can be easily produced. Morepractically, in a conventional device, the grating elements having threephase levels can be properly produced in an area where the gratingperiod is relatively large, but the grating elements having three phaselevels cannot be produced so as to have sharp-edged steps in an areawhere the grating period is relatively small. In the diffractive opticaldevice 10 in this example, only two phase levels are sufficient for thegrating elements 21 in an area where the grating period is less than 1.6times the wavelength of the incident light. Thus, precision processingis easier and the grating elements 21 can be produced as designed.

In this example, the number of phase levels is changed from two to threeat the normalized grating period of 1.6 (namely, when the grating periodis 1.6 times the wavelength of the incident light). Although the optimumnormalized grating period at which the number of phase levels should bechanged is different depending on the incident angle of light and thelike, it has been confirmed that substantially the same effects areobtained as long as the number of phase levels is changed at thenormalized grating period of between 1.5 and 3.

The other parameters of the diffractive optical device 10 in thisexample are, for example, as follows: The diameter of a circular openingis 1 mm; the wavelength of the incident light λ=is 0.6328 μm; theincident angle of light θ=20°; and the focal distance is 2.5 mm. In area2B where the number of phase levels is three, the grating period is, forexample, between 1.0 and 2.0 μm; and the height h_(B) is, for example,0.84 μm. In area 2A where the number of phase levels is two, the gratingperiod is, for example, between 0.89 μm and 1.0 μm; and the height h_(A)is, for example, 0.63 μm. The height of the grating element 21 ischanged in accordance with the number of phase levels, in which mannerthe diffraction efficiency is optimized. In area 2A, the duty ratio d1/ΛA (FIG. 4) is, for example, 0.3. The duty ratio is the ratio of an areaoccupied by a material other than air with respect to the total area ofone grating period in terms of the cross section of the grating section2.

The grating pattern shown in FIG. 5 will be described in detail. In anx-y coordinate shown in FIG. 5, where the wavelength of the incidentlight is λ, the refractive index of the substrate 1 is n and theincident angle of light is θ, the phase shift function is expressed by:

    Φ(x,y)=k((x.sup.2 +y.sup.2 +f.sup.2).sup.1/2 +ny sin θ-f)-2mπk=λ/2π;

and m is an integer fulfilling 0≦Φ≦2π and indicates the order of thegrating pattern. From such phase shift function, the shape of the arc ofthe grating section 2 having an order of m is a top part of an ellipsein which the center is expressed by:

    (0,-n sin θ(mλ+f)/(1-n.sup.2 sin.sup.2 θ),

the length of a minor axis (axis x) is expressed by:

    d.sub.x =2(m.sup.2 λ.sup.2 +2mλf+n.sup.2 f.sup.2 sin.sup.2 θ).sup.1/2 /(1-n.sup.2 sin.sup.2 θ).sup.1/2,

and the length of a major axis (axis y) is expressed by:

    d.sub.y =d.sub.x /(1-n.sup.2 sin.sup.2 θ).sup.1/2,

Needless to say, the grating pattern of a diffractive optical deviceaccording to the present invention is not limited to the one shown inFIG. 5, but can be arbitrarily designed in accordance with the use.

The substrate 1 and the grating section 2, which allow transmissiontherethrough of light to be diffracted are formed of, for example, glassor a synthetic resin. In the case that infrared light is used, thesubstrate 1 and the grating section 2 may be formed of a semiconductormaterial such as Si or GaAs.

The diffractive optical device 10 in the first example is produced by anelectron beam drawing method. According to this method, the substrate 1is coated with a synthetic resin such as an electron beam resist (forexample, PMMA or CMS) which is sensitive to an electron beam, and anelectron beam is radiated to the layer of the synthetic resin. Inaccordance with the shape of the cross section of the diffractiveoptical device to be produced, the amount of the electron beam to beradiated is controlled. For example, when a positive resist is used, theelectron beam is radiated in a smaller amount to an area which isrelatively thick so as to increase the ratio of the thickness remainingafter the development with respect to the thickness before development.After the electron beam radiation, the resultant laminate is developedto produce the diffractive optical device 10. A diffractive opticaldevice according to the present invention may be produced with any otherspecifications suitable for the use.

For the purpose of mass-production, the diffractive optical devices maybe produced at a lower cost by forming a mold by a nickel electroformingmethod and duplicating the mold using a UV curable resin. Especiallydiffractive optical devices arranged in an array can be produced at ahigh precision with uniform characteristics at one time in this manner.The grating section 2 formed of a synthetic resin such an electron beamresist may be transferred onto the substrate 1 formed of glass or thelike by ion beam etching. In such a case, the diffractive optical deviceis stable in performance against temperature change.

As is described above, in the case when light is incident at an offsetangle with respect to the vertical direction to the surface of thesubstrate 1, the diffraction efficiency does not necessarily increase asthe numbers of phase levels increases in the entire area of the gratingsection 2. The diffraction efficiency has a peak at different number ofphase levels in accordance with the grating period. Accordingly, bysetting the number of phase levels of the grating elements to be optimumin accordance with the grating period, the diffraction efficiency can behigh in the entire diffractive optical device 10. Moreover, since theoptimum number of phase levels tends to decrease as the grating perioddecreases in an area where the grating period is relatively small, eventhe grating elements having a small grating period can be easilyfabricated.

EXAMPLE 2

With reference to FIG. 8, a diffractive optical device 20 in a secondexample according to the present invention will be described. FIG. 8 isa plan view of the diffractive optical device 20. Identical elementswith those in the first example will bear identical reference numeralstherewith, and explanation thereof will be omitted.

In the second example, grating elements 22 in the grating section 2provided on the substrate 1 are straight lines in shape extending in thedirection of axis x. The grating period changes in the direction of axisy. The diffractive optical device 20 having such grating elements 22 isused as a cylindrical off-axis lens for collecting light incident at anoffset angle with respect to the vertical direction to the surface ofthe substrate 1 only in the direction of one axis. In the example shownin FIG. 8, the light is collected in the direction of axis y.

The diffractive optical device 20 has a similar cross sectional view asthat of the diffractive optical device 10 shown in FIG. 4. In thediffractive optical device 20, the same effects as obtained in the firstexample can be obtained by providing the grating elements 22 havingthree phase levels in area 2B' where the grating period is relativelylarge and providing the grating elements 22 having two phase levels inarea 2A' where the grating period is relatively small.

EXAMPLE 3

With reference to FIGS. 9 through 11, a diffractive optical device 30 ina third example according to the present invention will be described.FIG. 9 is a cross sectional view illustrating a basic structure of thediffractive optical device 30. FIG. 10 is a graph illustrating therelationship between the normalized grating period and the efficiency offirst order diffraction when the incident angle of light is 20°. FIG. 11is a graph illustrating the relationship between the normalized gratingperiod and the efficiency of first order diffraction when the incidentangle of light is 30°. Identical elements with those in the firstexample will bear identical reference numerals therewith, andexplanation thereof will be omitted.

The diffractive optical device 30 is an off-axis lens in which thegrating period changes toward one direction. The grating section 2including grating elements 23 are divided into four areas 2A" through2D". In area 2D" where the grating period is largest among in the fourareas, each grating element 23 has five phase levels. The gratingelements 23 each have four phase levels in area 2C" where the gratingperiod is second largest, three phase levels in area 2B" where thegrating period is second smallest, and two phase levels in area 2A"where the grating period is smallest among in the four areas.

As is understood from FIG. 10, area 2A" has a normalized grating periodof, for example, 1.2≦Λ/λ<1.6. Area 2B" has a normalized grating periodof, for example, 1.6≦Λ/λ<3.1. Area 2C" has a normalized grating periodof, for example, 3.1≦Λ/λ<4.7. Area 2D" has a normalized grating periodof, for example, 4.7≦Λ/λ<5.5. The height of each area is, for example,0.633 μm in area 2A", 0.84 μm in area 2B", 0.95 μm in area 2C", and 1.01μm in area 2D". The other parameters of the diffractive optical device30 are, for example, as follows: The diameter of a circular opening is 1m; the wavelength of the incident light λ=0.6328 μm; and the incidentangle of light θ=20°. The focal distance is 1.4 mm, which is shorterthan that of the off-axis lens 10 in the first example. In an off-axislens having such a short focal distance, the grating period changes at ahigher ratio.

As is shown in FIG. 10, the diffraction efficiency of the gratingelements having five phase levels becomes lower than the diffractionefficiency of the grating elements having four phase levels at thenormalized grating period of 4.7. The diffraction efficiency of thegrating elements having four phase levels becomes lower than thediffraction efficiency of the grating elements having three phase levelsat the normalized grating period of 3.1. Similarly, the diffractionefficiency of the grating elements having three phase levels becomeslower than the diffraction efficiency of the grating elements having twophase levels at the normalized grating period of 1.6. Accordingly, byproviding the grating elements 23 having the optimum phase levels foreach area, the diffraction efficiency can be high in the entirediffractive optical device 30.

FIG. 11 shows the relationship between the normalized grating period andthe efficiency of first order diffraction when the incident angle oflight is 30°. In the case that the incident angle of light changes, theoptimum normalized grating period at which the number of phase levelsshould be changed is also changed. Nonetheless, the inventors of thepresent invention have confirmed that the same effects are obtained aslong as the number of phase levels is changed from five to four at thenormalized grating period of between 4 and 7, from four to three at thenormalized grating period of between 2 and 5, and from three to two atthe normalized grating period of between 1.5 and 3.

In the above example, an off-axis lens for collecting light incident atan offset angle vertically is described. The present invention providesthe same effects in other types of diffractive optical devices in thecase that the light is incident at an offset angle.

EXAMPLE 4

With reference to FIGS. 12 through 17, a diffractive optical device 40in a fourth example according to the present invention will bedescribed. FIG. 12 is a cross sectional view of the diffractive opticaldevice 40, and FIG. 13 is a plan view thereof. Identical elements withthose in the first example will bear identical reference numeralstherewith, and explanation thereof will be omitted.

As is appreciated from FIGS. 12 and 13, the diffractive optical device40 has a similar plan view with that of the diffractive optical device10 in FIG. 5 but has a different cross sectional view from that of thediffractive optical device 10. Grating elements 24 in the gratingsection 2 each have a rectangular cross sectional view. The duty ratiod/Λ changes in accordance with the grating period. Symbol Λ denotes thegrating period, and symbol λ denotes the wavelength of the light. Theduty ratio is the ratio of an area occupied by a material other than airwith respect to the total area of one grating period in terms of thecross section of the grating section 2.

In the case that the light to be diffracted is transmitted through thesubstrate 1 to reach the grating section 2, where the wavelength of thelight to be diffracted in the vacuum is λ, each grating period Λ is setto be larger than λ/2.

In the case of a reflection type diffractive optical device in which thelight to be diffracted is reflected by a reflective layer which isformed over the grating section 2, where the wavelength of the light tobe diffracted in the vacuum is λ, and the refractive index of thesubstrate 1 is n, each grating period Λ is set to be larger than λ/2n.

In the fourth example, the duty ratio is set for 0.5 in an area wherethe grating period is relatively large and to be reduced incorrespondence with decrease in the grating period. (The duty ratio willbe described in detail later.) The height h of the grating elements 24is constant regardless of the grating period. The other parameters ofthe diffractive optical device 40 are, for example, as follows: Thediameter of a circular opening is 1 mm; the wavelength of the incidentlight λ=0.6328 μm; and the incident angle of light 74 =20°. The gratingperiod is, for example, 0.633 μm to 6.3 μm, and the height h of thegrating elements 24 is, for example, 0.63 μm.

According to the experiment performed by the inventors of the presentinvention, when light was incident at an offset angle with respect tothe vertical direction to the top surface of the substrate 1, thediffraction efficiency was highest at the duty ratio of approximately0.5 in an area having a relatively large grating period. The inventorshave found that the diffraction efficiency increases as the duty ratiodecreases in an area where the grating period is proximate to thewavelength of the incident light. The experiment will be described indetail, hereinafter.

FIG. 14 illustrates the relationship between the normalized gratingperiod and the efficiency of first order diffraction when the incidentangle of light is 20° and the refractive index of the grating section 2is 1.5. As is indicated by the solid line in FIG. 14, when the dutyratio is 0.5, the diffraction efficiency is approximately 40% in an areawhere the grating period is relatively large, but is reduced in an areawhere the normalized grating period is as small as 3. When the dutyratio is 0.4 (chain line) and 0.3 (dashed line), the diffractionefficiency is lower than that in the case when the duty ratio is 0.5 inan area where the grating period is relatively large, but is higher thanthat in the case when the duty ratio is 0.5 in an area where the gratingperiod is relatively small.

FIG. 15 illustrates the relationship between the normalized gratingperiod and the efficiency of first order diffraction when the incidentangle of light is 30°. The results are substantially the same as thoseshown in FIG. 14, namely, the diffraction efficiency has a peak atdifferent duty ratios in accordance with the grating period.

Accordingly, by changing the duty ratio in accordance with the gratingperiod, the diffraction efficiency can be high in the entire diffractiveoptical device 40.

In this example, the duty ratio is set as shown in FIG. 16 in relationwith the grating period. The duty ratio is 0.45 to 0.5 in an area wherethe grating period is relatively large, and the duty ratio is changed asshown in FIG. 16 in an area where the grating period is relativelysmall. The curve indicating the optimum duty ratio depends on variousconditions. The duty ratio is desirably less than 0.5 in an area wherethe normalized grating period is smaller than 3 to 4. In general, thediffraction efficiency is improved by gradually reducing the duty ratioin correspondence with decrease in the grating period.

As is shown in FIG. 17, the diffractive optical device 40 is used as anoff-axis lens. As is shown in FIG. 17, the light 5 which is propagatedzigzag in the light guide region 12 in the substrate 1 goes out throughthe top surface of the substrate 1 as outgoing light 6. The light guideregion 12 is provided with the reflective layers 4A and 4B respectivelyon the top surface and the bottom surface thereof for reflecting thelight 5 alternately in repetition. Thus, the light 5 is propagatedzigzag and finally goes out above the substrate 1 vertically.

As is shown in FIG. 13, the grating pattern is symmetrical with respectto the center thereof, and arcked toward one direction. The gratingperiod gradually decreases and the curvature of the grating elements 24increases toward such a direction.

The materials for each component of the diffractive optical device 40and a method for producing the same are identical with those describedin the first example, and explanation thereof will be omitted.

EXAMPLE 5

With reference to FIG. 18, a diffractive optical device 50 in a fifthexample according to the present invention will be described. FIG. 18 isa plan view of the diffractive optical device 50. Identical elementswith those in the fourth example will bear identical reference numeralstherewith, and explanation thereof will be omitted.

In the fifth example, grating elements 25 in the grating section 2provided on the substrate 1 are straight lines in shape extending in thedirection of axis x. The grating period changes in the direction of axisy. The diffractive optical device 50 having such grating elements 25 isused as a cylindrical off-axis lens for collecting light incident at anoffset angle with respect to the vertical direction to the surface ofthe substrate 1 only in the direction of one axis. In the example shownin FIG. 18, the light is collected in the direction of axis y.

The diffractive optical device 50 has a similar cross sectional view asthat of the diffractive optical device 40 shown in FIG. 12. In thediffractive optical device 50, the same effects as obtained in thefourth example such as improvement in the diffraction efficiency can beobtained by changing the duty ratio in the same manner as in the fourthexample.

EXAMPLE 6

With reference to FIGS. 19 and 20, a diffractive optical device 60 in asixth example according to the present invention will be described. FIG.19 is a cross sectional view of the diffractive optical device 60, andFIG. 20 is a graph illustrating the relationship between the normalizedgrating period and the efficiency of first order diffraction. Identicalelements with those in the fourth example will bear identical referencenumerals therewith, and explanation thereof will be omitted.

As is shown in FIG. 19, grating elements 26 in the grating section 2 arearranged with different duty ratios as well as with different heights.As is shown in FIG. 20, in an area where the normalized grating periodis 3 or more, the grating elements 26 have an identical height. In anarea where the grating period is less than 3, the height of the gratingelements 26 is changed so as to have substantially a uniform diffractionefficiency. Although the curve indicating the optimum height depends onthe various conditions, the height is desirably changed in an area wherethe normalized grating period is less than 3 to 4.

In general, the diffraction efficiency is improved by reducing theheight of the grating elements 26 in correspondence with decrease in thegrating period. In this example, the duty ratio and the height of thegrating elements 26 are changed in accordance with the grating period soas to prevent deterioration in the diffraction efficiency even in anarea where the grating period is small. Accordingly, the diffractionefficiency is substantially uniform in the entire diffractive opticaldevice 60. As a result, light distribution in a spot where the light iscollected can be constant.

In the above examples, the diffractive optical devices are each anoff-axis lens for collecting the light vertically, the light beingincident at an offset angle with respect to the vertical direction tothe surface of the substrate 1. The present invention provides the sameeffects in various other diffractive optical devices in the case whenthe light is incident at an offset angle.

In the first through the third examples, the duty ratio may be changedin accordance with the grating period in an area where the number of thephase levels is two.

In the above examples, the diffractive optical devices of a transmissiontype are described. The present invention is also applicable toreflection type devices having a reflective film provided on the gratingsection 2. FIG. 21 is a cross sectional view of such a reflection typediffractive optical device 70 provided with a reflective film 7. As thereflective film 7, the one used in a conventional diffractive opticaldevice may be used.

Films other than the reflective film, for example, a non-reflective filmsuch as a protective thin film or a thin film for preventing reflectionmay be used instead of the reflective film 7. The thin film forpreventing reflection is used in a transmission type device.

The grating elements are separated from one another in the aboveexamples, but may be connected together at the bottom thereof. FIG. 22is a cross sectional view of such a diffractive optical device 80. Thetop surface of the substrate 1 is not exposed.

FIG. 23 is a cross sectional view of a diffractive optical device 90having a grating pattern formed using a positive resist. The shape ofgrating elements substantially contributing to diffraction is the samewhether a negative or a positive resist is used.

According to the present invention, as has been described so far, thenumber of the phase levels changes in accordance with the gratingperiod. By such a structure, the diffraction efficiency is improved inthe entire device, especially for light incident at an offset angle withrespect to the vertical direction to the top surface of the substrate.By reducing the optimum number of phase levels in accordance withdecrease in the grating period, the grating elements are easily producedeven in an area where the grating period is relatively small.

In the case when the grating elements each have a rectangular crosssection, the duty ratio regarding each cross section is set to beoptimum in accordance with the grating period. In this manner, thediffraction efficiency of the light incident at an offset angle isimproved even in an area where the grating period is relatively small.Further, by changing the height of the grating elements as well as theduty ratio in accordance with the grating period, the diffractionefficiency can be uniform in the entire device. As a result, lightdistribution in a spot where the light is collected can be constant.

Various other modifications will be apparent to and can be readily madeby those skilled in the art without departing from the scope and spiritof this invention. Accordingly, it is not intended that the scope of theclaims appended hereto be limited to the description as set forthherein, but rather that the claims be broadly construed.

What is claimed is:
 1. A diffractive optical device, comprising:asubstrate for allowing transmission therethrough of light to bediffracted; and a grating section located on the substrate and includinga plurality of grating elements arranged in a disposition plane in acontinuous grating pattern which collects light incident at an offsetangle with respect to a direction normal to the disposition plane, saidcontinous grating pattern having a plurality of grating periods withinthe continuous grating pattern, wherein the smallest grating period isgreater than 1/2 n of the wavelength of said light where n is therefractive index of the substrate, said plurality of grating elementsincluding:a first plurality of grating elements having a first dutyratio, the first plurality of grating elements having a first gratingperiod which results in a first diffraction efficiency with said lightbeing incident at said offset angle, and a second plurality of gratingelements having a second duty ratio different from the first duty ratio,said second plurality of grating elements having a second grating periodwhich results in a second diffraction efficiency with said light beingincident at said offset angle, said first plurality of grating elementsarranged such that said first grating period is smaller than said secondgrating period.
 2. A diffractive optical device according to claim 1wherein the duty ratio is less than 0.5 in an area where the gratingperiod is less than in other areas.
 3. A diffractive optical deviceaccording to claim 2, wherein the grating period decreases and the dutyratio becomes progressively smaller as the grating period decreases. 4.A diffractive optical device according to claim 1, wherein the gratingelements are arcs symmetrically arranged with respect to a centerthereof, and the grating period becomes progressively smaller in adirection away from said center.
 5. A diffractive optical deviceaccording to claim 1, wherein the plurality of grating elements areparallel straight lines, and the grating period changes in a directionwhich is perpendicular to said parallel straight lines.
 6. A diffractiveoptical device according to claim 1, wherein the grating section iscovered with a thin film.
 7. A diffractive optical device according toclaim 6, wherein the thin film is reflective.
 8. A diffractive opticaldevice according to claim 6, wherein the thin film is non-reflective. 9.A diffractive optical device according to claim 2, wherein the substrateincludes a light guide region for propagating the light.
 10. Adiffractive optical device according to claim 1, wherein the first dutyratio is smaller than the second duty ratio.
 11. A diffractive opticaldevice according to claim 1, wherein the plurality of grating elementshas a rectangular cross section.
 12. A diffractive optical deviceaccording to claim 1 wherein said first diffraction efficiency isdifferent from said second diffraction efficiency.